Measurement of residual and thermally-induced stress in a rail

ABSTRACT

In a railway line, thermally-induced stresses are a factor for both rail breaks and rail buckling. These stresses are in the longitudinal direction. A nondestructive measuring technique enables the residual stress in a rail to be determined, and hence the thermally-induced stress. An electromagnetic probe is used to measure the stresses in the rail web in the vertical direction, and in the direction parallel to the longitudinal axis. The residual stress in the longitudinal direction can be deduced from the measured stress in the vertical direction; hence the thermally-induced stress can be determined.

This invention relates to a method and apparatus for determiningresidual stress in a ferromagnetic object such as a rail of a railwayline, preferably using an electromagnetic probe.

The stresses in structures such as rails, bridges and pipelines, complexmechanisms such as vehicles and machinery, or simple devices such asstruts, cables or bearings arise from various causes including changesof temperature, and the loads and pressures due to use. There may alsobe residual stresses arising from the fabrication of the structure ordevice, and any bending that the structure or device was subjected toduring construction; the residual stresses arising from fabrication willalso be affected by any stress-relieving heat treatment. A way ofmeasuring stress in a steel plate is described in U.S. Pat. No.5,828,211 (GB 2 278 450), this method using a probe containing anelectromagnetic core to generate an alternating magnetic field in theplate, and then combining measurements from two sensors, one being ameasure of stress-induced magnetic anisotropy (SMA), and the other beinga measure of directional effective permeability (DEP). The probe isgradually turned around so the magnetic field has a plurality ofdifferent orientations in the plate, and these measurements are taken ateach such orientation. The probe enables the stress to be measured nearthe surface, the depth of penetration depending upon the frequency.

In the case of railway lines, thermally-induced stresses are acontributing factor for both rail breaks (when the rail temperaturefalls, for example in winter), and for rail buckling (when the railtemperature rises, for example in summer). Traditionally incontinuous-welded rail these problems are minimised by initiallyinstalling the rail in a state of tension, such that the thermalstresses would become zero if the rail temperature were to rise to a“stress-free temperature” which is selected such that in practice thethermal stresses do not reach excessive values. It would be desirable tobe able to monitor the thermally-induced stresses in a rail, but this isno simple matter. As a rule, stress measurement techniques measure thetotal stress, which is the sum of the thermally-induced stress and theresidual stress (as tensors); to determine the thermal stress it istherefore necessary to also ascertain the residual stress. This can bemeasured by measurements on a rail that is unconstrained, for example bycutting out a section of rail, but a nondestructive measurementtechnique would be desirable. (In this specification the term thermalstress or thermally-induced stress refers to the difference between thetotal stress and the residual stress.)

It will also be appreciated that accurate measurement of railtemperature is also very difficult to achieve, because of varyingenvironmental conditions along a length of rail and because of thecomparatively poor thermal conductivity of rail steel; an uncertainty inthe mean temperature of any less than about +/±2° C. would be difficultto achieve. Temperature measurements in sunshine are likely to be evenharder.

According to the present invention there is provided a method fordetermining the residual stress and the thermally-induced stress in arail, the method comprising measuring the stresses in part of the railremote from the railhead in a direction perpendicular to thelongitudinal axis of the rail, and in a direction parallel to thelongitudinal axis, determining from the stress in the perpendiculardirection an estimate of the residual stress in the parallel direction,and hence by comparing the measured stress in the parallel direction tothe estimated residual stress in the parallel direction determining thethermally-induced stress.

It has been discovered that residual stresses in rails vary from rail torail, and through the life of a rail. However the lifetime variation canbe minimised by considering stresses in regions remote from therailhead, that is to say in the web or possibly the foot of the rail.The residual stresses in both the parallel and perpendicular directionsare principally caused by the straightening which is the final stage ofmanufacture of the rail, and consequently can be related to each other.In the web, for example, the residual stresses are typicallycompressive, in the region 120 to 220 MPa in the parallel direction, and50 to 100 MPa in the perpendicular (vertical) direction. It should beappreciated that the variations in thermally-induced stress in theparallel direction in a straight track are only about 2.4 MPa/° C., sothat variations in the residual longitudinal stress arising from themanufacturing process of say 50 MPa are generally much larger than thethermally-induced stresses.

In one embodiment of the invention the stress in the perpendiculardirection is correlated with the residual stress in the paralleldirection; in an alternative embodiment, the stress in the perpendiculardirection is measured at different depths, and its variation with depthis correlated with the residual stress in the parallel direction. Thisalternative approach does not require absolute measurements of stress inthe vertical direction, but only the difference in stress for differentdepths, and this may be desirable.

Preferably the stress is measured using an electromagnetic probe. In thepreferred stress-measurement method the probe comprises an electromagnetmeans, means to generate an alternating magnetic field in theelectromagnet means and consequently in the rail, and a magnetic sensorarranged to sense a magnetic field due to the electromagnet means; andthe method comprises resolving signals from the magnetic sensor into anin-phase component and a quadrature component; mapping the in-phase andquadrature components directly into stress and lift-off components; anddeducing the stress from the stress component so determined.

The mapping requires a preliminary calibration, with a specimen of thematerial, to determine how the in-phase and quadrature components of thesignal vary with lift-off (at a constant stress) and vary with stress(at a constant lift-off), and deducing from the calibration measurementsthe applicable mapping for any stress and any lift-off. The mapping maybe represented in the impedance plane (i.e. on a graph of quadraturecomponent against in-phase component) as two sets of contoursrepresenting signal variation with lift-off (for different values ofstress) and signal variation with stress (for different values oflift-off), the contours of both sets being curved. The contours of oneset intersect the contours of the other set at non-orthogonal angles.Surprisingly it has been found that the angles at which the constantlift-off contours intersect any one contour of constant stress are allthe same. Hence measurements taken along a few contours of each setenable the positions of the other contours of each set to be determined.This method of interpreting the signals and distinguishing betweenstress and lift-off is described in detail in WO 03/034054.

Surprisingly this simple mapping has been found to give an accuraterepresentation of the variation of the signals with material property(e.g. stress), and provides a simple way to distinguish these variationsfrom variations arising from lift-off or other geometrical variationssuch as surface texture or curvature.

Preferably the electromagnet means comprises an electromagnetic core andtwo spaced apart electromagnetic poles, and the magnetic sensor ispreferably arranged to sense the reluctance (or flux-linkage) of thatpart of the magnetic circuit between the poles of the electromagnetmeans. It is also desirable to arrange for such measurements to be takenwith a plurality of different orientations of the magnetic field, at asingle location on the object. This may be achieved using a single probethat is rotated at that location, measurements being taken withdifferent orientations of the probe. The sensor provides a measure ofthe permeability of the material through which the flux passes betweenthe poles; the corresponding measurements at different probeorientations at a location on the object hence indicate the effectivepermeability in different directions.

The probe may also include a second magnetic sensor between the twopoles and arranged to sense magnetic flux density perpendicular to thedirection of the free space magnetic field between the poles. Thissecond sensor would detect no signal if the material were exactlyisotropic; however stress induces anisotropy into the magneticproperties of the material, and so the signals received by the secondsensor (or flux-rotation sensor) are a measure of this stress-inducedmagnetic anisotropy. The variations in the flux rotation signals atdifferent probe orientations, at a location on the object, enable thedirections of the principal stress axes to be accurately determined. Theflux rotation signals can also be related to the stress.

The probe may also include a third magnetic sensor (a flux-leakagesensor) between the poles arranged to sense magnetic flux densityparallel to the free space magnetic field. This third sensor detectsflux leakage which is influenced by changes in material properties,lift-off, and cracks. As with the flux-linkage sensor, measurements at alocation are preferably made at different probe orientations.

The reluctance (or flux-linkage) signal from the probe is preferablybacked-off, i.e. processed by first subtracting a signal equal to thesignal from that sensor with the probe adjacent to a stress-freelocation. The backed-off signal is then amplified so the small changesdue to stress are easier to detect. This backing off is performed afterresolving into in-phase and quadrature components but before correctingfor lift-off, for example by the mapping described above. Preferably thesignals from the probe are digitized initially, and the backing-off andthe lift-off correction are performed by analysis of the digitalsignals.

Generally, the more different probe orientations are used for takingmeasurements the more accurate the determination of stress levels canbe. The measurements at different probe orientations at a particularlocation would usually be obtained by rotating the probe, butalternatively might be obtained using an array of probes of differentorientations that are successively moved to that location. It will beappreciated that measurements of stress at different depths below thesurface, where this is required, may be achieved by generating thealternating magnetic field with different frequencies.

The invention will now be further and more particularly described, byway of example only, and with reference to the accompanying drawings, inwhich:

FIG. 1 shows a diagrammatic view of an apparatus for measuring stress;

FIG. 2 shows a longitudinal sectional view of a probe for use in theapparatus of FIG. 1;

FIG. 3 shows graphically the variation of the backed-off quadrature andin-phase components of flux linkage with variations of lift-off, andwith variations of stress; and

FIG. 4 shows graphically the correlation between the signalsrepresenting stress in the vertical and longitudinal directions in railwebs.

Referring to FIG. 1, a stress measuring apparatus 10 includes a sensorprobe 12 comprising sensors for flux-linkage, flux-rotation andflux-leakage, the probe 12 being attached to an electric motor 14 whichcan be held by an operator, so the motor 14 can turn the probe 12 withone end adjacent to a surface of a steel object 16 (the web of a rail inthis case) in which the stresses are to be determined. The sensor probe12 and motor 14 are connected by a 2 m long umbilical cable 17 to asignal conditioning/probe driver unit 18. The unit 18 is connected by along umbilical cable 19 (which may for example be up to 300 m long) toan interface unit within a microcomputer 20, which has a keyboard 21.Operation of the apparatus 10 is controlled by software in themicrocomputer 20.

Referring now to FIG. 2, the probe 12 is shown detached from the motor14, in longitudinal section although with the internal components shownin elevation (the connecting wires within the probe 12 are not shown).

The probe 12 comprises a cylindrical brass casing 24 of externaldiameter 16.5 mm and of overall height 60 mm, the upper half being ofreduced diameter whereby the probe 12 is attached to the motor 14. Theupper half of the casing 24 encloses a head amplifier 25. The lower halfencloses a U-core 26 of laminated mu-metal (a high permeabilitynickel/iron/copper alloy) whose poles 28 are separated by a gap 7.5 mmwide, and are each of width 2.5 mm, and of thickness 10 mm (out of theplane of the figure). The poles 28 are in the plane of the lower end ofthe casing 24, which is open. Around the upper end of the U-core 26 is aformer on which are wound two superimposed coils 30. One coil 30 a(which has 200 turns) is supplied with the sinusoidal drive current fromthe unit 18; the other coil 30b (which has 70 turns) provides fluxlinkage signals.

Between the two poles 28 is a former on which is wound a 1670-turnrectangular coil 32, about 4 mm high and 6 mm wide, and 6 mm-square asseen from below, the windings lying parallel to the plane of the figureso the longitudinal axis of the coil 32 is perpendicular to the linebetween the centres of the poles 28. The coil 32 is supported by asupport plate 34 fixed between the arms of the U-core 26 so the lowerface of the coil 32 is in the plane of the poles 28. The coil 32provides the flux-rotation signals. If a flux-leakage signal isrequired, a coil may be wound on the same former but with windingsperpendicular to the plane of the figure. All the signals are amplifiedby the head amplifier 25 before transmission to the unit 18.

In operation of the system 10, the motor 14 is supported so the lowerend of the probe 12 is adjacent to the surface of a steel object and thelongitudinal axis of the probe 12 is normal to the surface. Analternating current of the desired frequency and amplitude is suppliedto the drive coil 30 a, so the magnetic field in the object 16oscillates about zero with an amplitude much less than saturation. Toset up the system 10, measurements are first made using an object of thesame type of steel as the rail 16 but in which the stresses arenegligible. The in-phase and quadrature components of the flux linkagesignal (i.e. the component in phase with the drive current, and thecomponent differing in phase by 90°) received by the microcomputer 20are each backed off to zero, and the backing off values are then fixed.During all subsequent measurements the flux linkage components arebacked off by these same amounts (i.e. subtracting a signal equal to thecomponent observed at a stress-free location).

Stress measurements can be taken by placing the probe 12 adjacent to theweb of the rail 16. The orientation of the line joining the centres ofthe poles 28 (referred to as the orientation of the probe 12) is notedrelative to a fixed direction on the surface. The motor 14 is thenenergized to rotate the probe 12, for example in a step-wise fashion 100at a time through a total angle of 360°. At each orientation of theprobe 12 all the signals are measured.

It will be appreciated that the procedure of the invention is applicablewith many different probes. The probe 12 might for example be modifiedby using a U-core 26 of a different material such as silicon iron (whichcan provide higher magnetic fields), or indeed the drive coil might beair-cored. The probe might be of a different shape or size; probesranging in size between about 3 mm and 75 mm have been used fordifferent purposes. In particular, for measurements on rails, a probe ofdiameter in the range 20 mm to 40 mm, e.g. 30 mm, would be suitable.

The flux rotation signals vary sinusoidally with probe orientation, sothe orientation at which they have their maxima and minima can bedetermined. The directions midway between these two orientations are thedirections of the principal stress axes. Measurements of flux rotationare therefore useful if the principal stress directions are unknown. Thevalues of flux linkage and flux leakage also vary sinusoidally withprobe orientation (in antiphase with each other), and the values areobserved at the principal stress directions. If the principal stressdirections are already known, then the probe 12 might instead be merelyoriented to those directions, and the measurements made; no rotation ofthe probe 12 would be necessary.

The values of the stresses in the web in the vertical (i.e.perpendicular to the longitudinal axis) and longitudinal directions canbe determined from the experimental measurements of flux linkage withthe probe 12 oriented in those directions. This requires calibration ofthe apparatus 10, taking measurements on a sample of material of thesame type as that of the rail 16, while subjecting it to a variety ofdifferent stresses. This may be done with a rectangular strip sample ina test rig, flux linkage measurements being made at the centre of thesample where the principal stress direction is aligned with the axis ofthe test rig. Referring to FIG. 3 this shows the backed-off flux-linkagein-phase and quadrature components obtained in such a test rig, themeasurements being made with a drive frequency of 70 Hz, and thespecimen being a steel bar. A first set of measurements were made atprogressively larger values of lift-off, L, but with no stress, S. Thisgives the lift-off contour A, the lift-off varying between 0 and 220microns. Similar lift-off contours A are obtained for other fixed valuesof stress, those for S=250 MPa tension and compression being shown.Measurements were then made at a range of different fixed values oflift-off, L, with varying stresses, S (both compression and tension),providing the contours B.

It will be appreciated that the contours A are curved, and the contoursB are not orthogonal to the contours A, but that they intersect atsubstantially constant angles along any one lift-off contour A.Consequently it is only necessary to make calibration measurementssufficient to plot a few such contours A and B, and the shapes of theother contours can be predicted.

After calibrating the probe 12 in this manner, measurements of stresscan be readily made from observations of flux linkage signals (resolvedand backed off), as the contours enable the changes due to lift-off tobe readily distinguished from changes due to stress. Any particularposition in the impedance plane (i.e. in the graph of quadrature againstin-phase components) corresponds to a particular value of stress and aparticular value of lift-off. The mapping between (in-phase, quadrature)coordinates and (stress, lift-off) coordinates may be carried outgraphically, referring to such contours, or by calculation. For exampleif the flux linkage signal has the in-phase and quadrature components ofthe position marked X, this corresponds to a lift-off of about 80microns and a stress of about 125 MPa. Alternatively this value X may betranslated (along the broken line Y) along a contour A of constantstress to find the in-phase and quadrature components at position Z thatwould be obtained with zero lift-off.

The value of stress found in this way is, it will be appreciated, theuniaxial stress that would provide that value of the flux linkagesignal. If the stresses are actually biaxial, then a further calibrationmust be carried out with a cross-shaped sample in a test rig, fluxlinkage measurements being made at the centre of the sample where theprincipal stress directions are aligned with the axes of the test rig.Hence a graph or map may be obtained for a range of values of stress onone axis (say the x-axis) and for a range of values of stress in theother axis (say the y-axis), with contours each of which shows thevalues of biaxial stress that give a particular value of apparentuniaxial stress along the x-axis; and a similar graph may be obtainedwith contours showing values of biaxial stress that give a particularvalue of apparent uniaxial stress along the y-axis. Hence frommeasurements of apparent uniaxial stress along the two principal stressaxes obtained as described earlier, the biaxial stress can bedetermined.

It will again be appreciated that the biaxial stress may be determinedeither graphically or by calculation in this way. Apparent values ofuniaxial stress (in MPa) may be used for this purpose, or alternativelythe numerical value of the flux linkage signal (in mV), either thein-phase or quadrature value, obtained by eliminating the effect oflift-off as described in relation to FIG. 3, may be used. Although theabove method of correcting for lift-off has been described in relationto flux-linkage signals it is equally applicable to flux-leakagesignals.

In the case of rail steels it has been found that the signals, ifcorrected for lift-off (for example as described above), both those forflux-linkage and those for flux-leakage, can be related almost linearlyto the stress. (It will be appreciated that the flux-leakage signalsincrease as the flux-linkage signal decrease.) Measurements have beentaken on nine different rails of different ages and from differentmanufacturers, on cut sections so that there is no thermally-inducedstress; each section of rail was 3 m long or longer, and of the samegrade of steel (220 grade) and cross-section (BS 113A). All themeasurements were taken more than 0.3 m from either end to avoid thoseregions in which the residual stresses may have relaxed, and severaldifferent measurements were taken on each rail, along its length. Therehas been found to be a clear positive correlation between the signals inthe longitudinal and vertical directions (i.e. parallel andperpendicular to the longitudinal axis), and so between the residualstresses in the longitudinal and vertical directions.

Referring now to FIG. 4, this shows graphically the flux linkage signalin the vertical direction (L1) and the flux linkage signal in thelongitudinal direction (L2), each signal having been corrected forlift-off, the crosses showing the mean values for the measurements takenalong each one of the nine different rail specimens, and the standarddeviation of the discrepancies from the straight line P; the scatteralong the straight line P is not indicated. (The numerical values on theaxes are proportional to the signal voltages, 10 on the scalecorresponding to 23 mV.) The positive correlation is clearly evident,and the straight line graph P may be represented by the equation:L 1=1.398 L 2+30.04This experimentally-observed relationship between the vertical andlongitudinal flux-linkage signals corresponds to a linear relationshipbetween the vertical and longitudinal residual stresses. By measuringthe stress in the vertical direction in a rail that is in situ (and inwhich there therefore may be thermally-induced stresses), thisrelationship enables the residual stress in the longitudinal directionto be determined. The difference between this and the observed totalstress in the longitudinal direction consequently represents what isreferred to as the thermally-induced stress.

The diamonds Q1, Q2 and the squares R1 and R2 on the graph showmeasurements made on a single rail in situ at different places along therail after repeated cutting, re-stressing, and welding. The diamond Q1shows the measurements on the rail before cutting, and Q2 shows themeasurements after the rail has been cut. In this cut condition the railis free standing, and there should therefore be no thermally-inducedstress. As expected, Q2 lies very close to the straight line graph P.The square R1 shows the measurements at a different position on the samerail, after the rail has subsequently been restressed and welded, and R2shows the measurements after the rail has again been cut. Once again, inthe cut condition, one would expect there to be no thermally-inducedstress; this is confirmed by the proximity of R2 to the straight line P.

It will thus be appreciated that from measurements such as Q1, the totallongitudinal stress corresponds to the value L2=−11.6; without cuttingthe rail you can predict that the residual stress corresponds to thevalue L2=−15.3 (ie the L2 value on the line P at the same value of L1).Consequently the thermally-induced stress corresponds to the differencebetween these two values. The thermal stress can be expressed in termsof the stress-free temperature, for example by assuming that thelongitudinal stress changes by 2.4 MPa/° C.; the faint lines parallel tothe line P each represents a difference of 10° C. between themeasurement temperature and the stress free temperature. For example, Q1corresponds to a stress free temperature about 15° C. above themeasurement temperature, while R1 corresponds to a stress freetemperature about 20° C. above the measurement temperature.

Measurements of the stress free temperature made in this way can becompared to those measured using a strain gauge and cutting the rail. Inone case, for example, measurements of the stress free temperaturedetermined as described above gave results of 24° C. and 31° C., whilethe stress free temperature determined using the strain gauge and railcutting gave results of 26° C. and 28° C.

The measurements taken above utilise flux linkage, but alternativelyflux leakage signals could have been used.

The above signals were taken at 70 Hz, but alternatively themeasurements might be made at a different frequency. In each case therewill be a similar relationship between the vertical and longitudinalresidual stresses. However, measurements at a higher frequency such as500 Hz penetrate to a shallower depth into the rail, and this has beenfound to give a steeper straight line P, because the vertical stressesare greater nearer the surface. Any instability in the performance ofthe instrument tends to affect measurements of vertical and longitudinalstress equally, so the frequency is preferably selected to provide astraight line P whose gradient is 1.0; such instabilities would thenmove the measured point parallel to the line P, and so would not affectthe accuracy of the measurement of stress free temperature.

In a further alternative, the residual longitudinal stresses may becorrelated with the variation of vertical stress with depth. Frommeasurements taken at several different frequencies, it is possible todeconvolve the measurements by assuming a functional form for thevariation with depth (as described in US 2003/0071614A) and obtainvalues for the vertical stress at different depths. This can enable theexact variation of stress with depth to be determined. More simply,measurements might be taken at say two different frequencies, and thedifference between those measurements correlated with the longitudinalstress measurements.

It will be appreciated that the present invention enables thestress-free temperature to be determined in a non-destructive fashion.It is applicable on both straight and curved tracks; it does not requirethe rail to be disconnected from the sleepers; and it is applicablewhether the rail is under tension or compression.

1. A method for determining the residual stress and thethermally-induced stress in a rail, the method comprising measuring thestresses in part of the rail remote from the railhead in a directionperpendicular to the longitudinal axis of the rail, and in a directionparallel to the longitudinal axis, determining from the stress in theperpendicular direction an estimate of the residual stress in theparallel direction, and hence by comparing the measured stress in theparallel direction to the estimated residual stress in the paralleldirection determining the thermally-induced stress.
 2. A method asclaimed in claim 1 wherein the stresses are measured in theperpendicular and longitudinal directions in the web of the rail.
 3. Amethod as claimed in claim 1 wherein the stresses are measured using anelectromagnetic probe which comprises an electromagnet means comprisingan electromagnetic core and two spaced apart electromagnetic poles, andat least one magnetic sensor arranged to sense either the reluctance ofthat part of the magnetic circuit between the poles of the electromagnetmeans, or flux-leakage between the poles of the electromagnet means. 4.A method as claimed in claim 1 wherein the residual stress in thelongitudinal direction is determined from a correlation between it andthe stress in the perpendicular direction.
 5. A method as claimed inclaim 1 wherein the residual stress in the longitudinal direction isdetermined from a correlation between it and the variation with depth ofthe stress in the perpendicular direction.
 6. A method as claimed inclaim 4 wherein the stresses are measured using an electromagnetic probegenerating an alternating magnetic field, the frequency of thealternating magnetic field being selected such that the correlationbetween residual longitudinal stress and perpendicular stress can berepresented by a straight line graph of gradient
 1. 7. A method asclaimed in claim 5 wherein the stressed are measured using anelectromagnetic probe generating an alternating magnetic field, and thevariation with depth of the stress in the perpendicular direction isdetermined from measurements at two different frequencies of thealternating magnetic field.
 8. A method as claimed in claim 5 whereinthe stresses are measured using an electromagnetic probe generating analternating magnetic field, and the variation with depth of the stressin the perpendicular direction is determined by deconvolvingmeasurements made at several different frequencies of the alternatingmagnetic field.